Welch’s t-test: when distribution normal but variance unequal
Permutation test for two samples: when distribution not normal (but both groups should still have similar distributions and ~equal variance)
Mann-Whitney-Wilcoxon test: when distribution not normal and/or outliers are present (but both groups should still have similar distributions and ~equal variance)
Lecture 8: Overview
The objectives:
Decision errors
Data exploration and transformation
Exploratory graphical data analysis
Graphical testing of assumptions
Data transformation and standardization
Outliers
Decision errors
Even good studies can reach incorrect conclusions
“Decision errors”
Two types of decision errors
Want to know probability of making these errors
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Type I and Type II Errors
Type I error rate
α: wrongly reject H₀ when it’s true
α = 0.05 means a type I error rate of 5%
Type II error rate, β
wrongly fail to reject H₀ when it’s false
Power = 1-β: probability of correctly rejecting H₀ when H₁ is true
Inverse relationship between type I and type II error - but not straightforward
Result of chance - sample not representative of population
Which type of error is more dangerous?
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the dotted line is also the alpha = 0.05
Exploratory graphical data analysis
Graphical exploration is one of first steps in data analysis:
Detect data entry errors
Pattern exploration
Assess assumptions of tests
Detect outliers
Most important Q: shape of distribution?
Determined by density plots: “density of different values”